# Hypercube Graph

• Difficulty Level : Basic
• Last Updated : 14 Sep, 2022

You are given input as order of graph n (highest number of edges connected to a node), you have to find the number of vertices in a Hypercube graph of order n.

Examples:

```Input : n = 3
Output : 8

Input : n = 2
Output : 4```

In hypercube graph Q(n), n represents the degree of the graph. Hypercube graph represents the maximum number of edges that can be connected to a graph to make it an n degree graph, every vertex has the same degree n and in that representation, only a fixed number of edges and vertices are added as shown in the figure below: All hypercube graphs are Hamiltonian, hypercube graph of order n has (2^n) vertices, , for input n as the order of graph we have to find the corresponding power of 2.

Recursive Approach

## C++

 `// C++ program to find vertices in a hypercube``// graph of order n``#include ``using` `namespace` `std;` `// function to find power of 2``int` `power(``int` `n)``{``    ``if` `(n == 1)``        ``return` `2;``    ``return` `2 * power(n - 1);``}` `// driver program``int` `main()``{``    ``// n is the order of the graph``    ``int` `n = 4;``    ``cout << power(n);``    ``return` `0;``}`

## Java

 `// Java program to find vertices in``// a hypercube graph of order n``class` `GfG``{` `    ``// Function to find power of 2``    ``static` `int` `power(``int` `n)``    ``{``        ``if` `(n == ``1``)``            ``return` `2``;``        ``return` `2` `* power(n - ``1``);``    ``}``    ` `    ``// Driver program``    ``public` `static` `void` `main(String []args)``    ``{``        ` `        ``// n is the order of the graph``        ``int` `n = ``4``;``        ``System.out.println(power(n));``    ``}``}` `// This code is contributed by Rituraj Jain`

## Python3

 `# Python3 program to find vertices in a hypercube``#  graph of order n` `# function to find power of 2``def` `power(n):``    ``if` `n``=``=``1``:``        ``return` `2``    ``return` `2``*``power(n``-``1``)`  `# Driver code``n ``=``4``print``(power(n))`  `# This code is contributed by Shrikant13`

## C#

 `// C# program to find vertices in``// a hypercube graph of order n``using` `System;` `class` `GfG``{` `    ``// Function to find power of 2``    ``static` `int` `power(``int` `n)``    ``{``        ``if` `(n == 1)``            ``return` `2;``        ``return` `2 * power(n - 1);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ` `        ``// n is the order of the graph``        ``int` `n = 4;``        ``Console.WriteLine(power(n));``    ``}``}` `// This code is contributed by Mukul Singh`

## PHP

 ``

## Javascript

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Output

`16`

Iterative Approach

## Java

 `/*package whatever //do not write package name here */` `import` `java.io.*;` `// Java program to find vertices in``// a hypercube graph of order n``class` `GFG {``  ` `  ``// Function to find power of 2``    ``static` `int` `power(``int` `n)``    ``{``      ` `      ``if``(n==``0``) ``return` `0``;``      ` `      ``int` `pow = ``1``;``      ` `      ``for``(``int` `i=``1``;i<=n;i++){``          ``pow *= ``2``;``      ``}``      ` `      ``return` `pow;``    ``}``  ` `    ``public` `static` `void` `main (String[] args) {``         ``// n is the order of the graph``        ``int` `n = ``4``;``        ``System.out.println(power(n));``    ``}``}`

Output

`16`

Java Using Math.pow()

## Java

 `/*package whatever //do not write package name here */` `import` `java.io.*;` `// Java program to find vertices in``// a hypercube graph of order n``class` `GFG {``  ` `  ``// Function to find power of 2``    ``static` `int` `power(``int` `n)``    ``{``      ``return` `(``int``)Math.pow(``2``,n);``    ``}``  ` `    ``public` `static` `void` `main (String[] args) {``         ``// n is the order of the graph``        ``int` `n = ``4``;``        ``System.out.println(power(n));``    ``}``}`

Output

`16`

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